As you probably know, four tests must be met for a person to be your qualifying relative. The four tests are:

1.      Not a qualifying child test,

2.      Member of household or relationship test,

3.      Gross income test, and

4.      Support test.

See these pages from Publication 17 referring to Qualifying Relative and read the section closely.

Whether or not your mother could be considered a Qualifying Relative depends on the circumstances, but let me just say that it is unlikely that you will be able to consider her a Qualifying Relative for dependent purposes without being able to treat your father the same way, which will depend on a number of issues, like his income, who is actually supporting her and him, their citizenship, whether or not they file a joint return, and a host of other considerations explained in the Publication 17 reference above.

Please read the reference above and see if the examples clarify this for you.